So T'Pring ... was taking a big risk that the victor of Spock's battle didn't decide to drag her along and make her live on the Enterprise anyway.

I think it was pretty obvious that originally Stonn was going to be T'Pring's choice for her champian, selecting Kirk was a spur of the moment decision. For all the reasons she would later mention, plus she wouldn't have to risk her lover.

A Starfleet captain who knows nothing about the culture of their fellow Federation co-founders is bad enough, but a Starfleet doctor who knows nothing about Vulcan physiology despite having a half-Vulcan crew member is just ridiculous.

Nothing is likely an over-statement. If there were 150 members in Picard's time, I personally figure there were something like 35 - 50 in Kirk's time. That Kirk would reasonable have more than a passing knowledge of all of them is unlikely. Even the one that produced his first officer.

And it's also unlikely that McCoy knew "nothing," he just didn't know everything. Which is probably the story with many Federation Member species.

Jonas Grumby wrote:

And if you're tempted to counter that, taboo or not, Spock would have easily discussed it with his captain and best friend, then you need to rewatch "Amok Time."

I have found it odd through the years, that fans seem to assume that as soon as Kirk and McCoy returned to the Enterprise, they immediately spread the intimate details of pon farr to the entire galaxy. As Spock's friends they both would have kept their mouth's shut on the matter, if you choose your friends carefully, you can trust them with your secrets.